多元Hawkes过程的稀疏性检验
A sparsity test for multivariate Hawkes processes
AI总结：
该研究针对带标记多元Hawkes过程的维度间因果关系检验问题，提出大样本下的新估计流程与似然比检验，推导其渐近分布为卡方混合，并通过两项金融数据集应用验证了方法有效性。
摘要：
多元Hawkes过程（Multivariate Hawkes processes，MHP）是一类点过程，其中不同坐标的事件通过相互激发产生交互作用。MHP的加权邻接矩阵编码了关系的强度，其支撑集与该过程的交互因果图的支撑集一致。我们研究带标记MHP各维度间因果关系的检验问题。原假设为一组邻接系数联合为零，对应不存在交互作用；备择假设为这些系数为正，即相关交互作用确实存在。为此，我们在大量独立事件序列样本的场景下，提出了一种新的估计流程。我们构建了对应的似然比检验，并推导出检验统计量的渐近分布为卡方分布的混合。我们在金融数据集上开展了两项应用以验证方法的性能：第一项应用中，我们的检验揭示了零售在线拍卖中竞拍者策略偏离静态均衡的现象；第二项应用中，我们发现了影响德国日内电力价格动态的部分因素。
英文摘要：
Multivariate Hawkes processes (MHP) are a class of point processes in which events at different coordinates interact through mutual excitation. The weighted adjacency matrix of the MHP encodes the strength of the relations, and shares its support with the causal graph of interactions of the process. We consider the problem of testing for causal relationships across the dimensions of a marked MHP. The null hypothesis is that a joint group of adjacency coefficients are null, corresponding to the absence of interactions. The alternative is that they are positive, and the associated interactions do exist. To this end, we introduce a novel estimation procedure in the context of a large sample of independent event sequences. We construct the associated likelihood ratio test and derive the asymptotic distribution of the test statistic as a mixture of chi squared laws. We offer two applications on financial datasets to illustrate the performance of our method. In the first one, our test reveals a deviation from a static equilibrium in bidders' strategies on retail online auctions. In the second one, we uncover some factors at play in the dynamics of German intraday power prices.
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